Okay, this one I can do. As seeing as how the character from Ratchet & Clank isn't Ratchet, we've got some real exploits to take advantage of.
The way I see it, Qwark probably has more raw muscle, but Murray has better technique. So they both even out. But while Murray has far more courage and heart than brains, Qwark has has the opposite problem where his bloated ego and cowardice nature are his defining characteristics. This means Qwark will make a greater effort to protect himself, and probably try to rely on keeping distance between himself and Murray, trying to use a blaster whenever possible.
Qwark is probably a pretty good shot with his blaster, and we know that when cornered he must be able to punch his way out of a lot of scrapes. So I think Qwark may be the winner. Mostly because if you make Qwark truly fear for his own life (cornering him so to speak), he will probably muster up enough courage to get on the offensive, at which point he may be quite dangerous.
Besides, we know Sly characters have trouble dodging a good blaster shot (especially Murray), so unless we get a proper Sly-styled boss arena that gives Murray the necessary tools to defeat Qwark, Murray may very well be doomed.
It's hard to say for sure, because we know far more about Murray's adventures than Qwarks, as most of Qwark's adventures are stories. So I am open to the idea of Murray winning the battle. I just get the impression Qwark is probably a fairly formidable foe in the arena.